Differentiator for Noisy Sampled Signals with Best Worst-Case Accuracy

Hernan Haimovich*, Richard Seeber, Rodrigo Aldana-López, David Gómez-Gutiérrez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This letter proposes a differentiator for sampled signals with bounded noise and bounded second derivative. It is based on a linear program derived from the available sample information and requires no further tuning beyond the noise and derivative bounds. A tight bound on the worst-case accuracy, i.e., the worst-case differentiation error, is derived, which is the best among all causal differentiators and is moreover shown to be obtained after a fixed number of sampling steps. Comparisons with the accuracy of existing high-gain and sliding-mode differentiators illustrate the obtained results.
Original languageEnglish
Article number9448332
Pages (from-to)938-943
Number of pages6
JournalIEEE Control Systems Letters
Publication statusPublished - 2022


  • Differentiation
  • estimation
  • observers
  • optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Control and Systems Engineering

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